On the dependency of risks in the individual life model. (English) Zbl 0931.62089

Summary: The paper considers several types of dependencies between the different risks of a life insurance portfolio. Each policy is assumed to have a positive face amount (or an amount at risk) during a certain reference period. The amount is due if the policy holder dies during the reference period. First, we will look for the type of dependency between individuals that gives rise to the riskiest aggregate claims in the sense that it leads to the largest stop-loss premiums. Further, this result is used to derive results for weaker forms of dependency, where the only non-independent risks of the portfolio are the risks of couples.


62P05 Applications of statistics to actuarial sciences and financial mathematics
91B30 Risk theory, insurance (MSC2010)
Full Text: DOI


[1] Beard, R.E.; Perks, W., The relation between the distribution of sickness and the effect of duplicates on the distribution of deaths, Journal of the institute of actuaries, LXXV, 75-86, (1949) · Zbl 0039.15401
[2] Carriere, J.F.; Chan, L.K., The bounds of bivariate distributions that limit the value of last-survivor annuities, Transaction of the society of actuaries, XXXVIII, 51-74, (1986), (with discussion)
[3] Dhaene, J.; Goovaerts, M.J., Dependency of risks and stop-loss order, ASTIN bulletin, 26, 2, 201-212, (1996)
[4] Feilmeier, M.; Segerer, G., Einige anmerkungen zur ruckversicherung von kumulrisiken nach dem “verfahren strickler”, Blatter der DGVM, 611-630, (1980), 1980 · Zbl 0448.62080
[5] Frees, E.W.; Valdez, E.; Carriere, J.F., Annuity valuation with dependent mortality, (), 31-80, 1985.2
[6] Gerber, H.U., An introduction to mathematical risk theory, (), no. 8 · Zbl 0431.62066
[7] Goovaerts, M.J.; Kaas, R.; van Heerwaarden, A.E.; Bauwelinckx, T., ()
[8] Heilmann, W.-R., On the impact of independence of risks on stop-loss premiums, Insurance: mathematics and economics, 5, 197-199, (1986) · Zbl 0596.62111
[9] Kaas, R., How to (and how not to) compute stop-loss premiums in practice, Insurance: mathematics and economics, 13, 241-254, (1993) · Zbl 0800.62681
[10] Kremer, E., Ein modell zur tarifierung von kumulschadenexzedenten-vertragen in der unfallversicherung, (), 53-61, 1983 · Zbl 0513.62101
[11] Norberg, R., Actuarial analysis of dependent lives, (), 243-255, 1989, Heft 2 · Zbl 0691.62093
[12] Seal, H.L., A probability distribution of deaths at age x when policies are counted instead of lives, Skand. aktuar tidskr., 18-43, (1947), 1947 · Zbl 0029.37501
[13] Strickler, P., Ruckversicherung des kumulrisikos in der lebensversicherung, Transactions of the xvith ICA, Vol. 1, 666-679, (1960)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.